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Has anyone formulated a general solution to the time-independent Schrödinger equation in terms of the potential function V(r), and if so, what is it?

For any type of V(r).

So, instead of a differential equation, a direct relationship between the wavefunction and the potential.

For any type of V(r).

So, instead of a differential equation, a direct relationship between the wavefunction and the potential.

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